As others have pointed out, a plane certified by the FAA to carry 100-200 passengers won’t get “blown off course” by a strong wind. Additionally, no where in the United States will it take 1-2 months to find an aircraft that large. Especially with all the press attention is would certainly get. The NTSB would never allow that to happen.
This story is more plausible if it’s a small general aviation aircraft such as a Cessna 172. Piloted by a newly minted private pilot who flew VFR (visual flight rules) into IMC (instrument meteorological conditions aka clouds.) Lost radios and unable to navigate in the weather it crashes in the mountains. That’s the best I can think of if it has to be an aircraft.
Alternatively, as others have said, set this in the 40s or 50s in an area out west with very little radar coverage. Or in a country other than the United States. Like I’ve said before, however, that many passengers is going to be an issue. If a plane with 200 passengers goes missing, no matter where it is, people are going to search for it immediately. The only way it won’t be found is if it crashes into the ocean, and this wouldn’t work in your story.